Overview

Curve meshing is one of the main steps in the meshing process of planar, surface or volume domains. In fact, most of the automatic mesh generation methods in or build the desired covering up from the data of the boundary meshes delimiting the domain considered. In two dimensions and for surfaces, the boundary is naturally formed by a set of curves. In three dimensions, the boundary is formed by a set of surfaces whose boundaries again involve a set of curves.

As we have already seen, in terms of quality, the mesh of a domain is strictly dependent on the mesh of its boundary (Chapters 5 to 7).

From a topological point of view, a curve is a priori a one-dimensional entity. However, when it is a component of a higher-dimensional entity (a planar region, a surface or a boundary of a solid), it must be treated in a multi-dimensional space. Hence, any control at the level of the mesh of a domain of or , induces a similar control at the level of the curves of this domain. For instance, a size and/or directional specification concerning the mesh elements is translated into a specification onto the curves of the domain. Here, we again encounter a governed meshing problem, which is either isotropic or anisotropic. To a control based on considerations related to the envisaged application (a finite element computation) is added a control of a purely geometric nature. The desired mesh must be a...